A bid made in response to a previous bid by another party(noun)
To make a counterbid(verb)
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Use "counterbid" in a sentence
"Nasdaq OMX Inc. Chief Executive Robert Greifeld is determined to mount a counterbid for NYSE Euronext , say people close to him."
"*** Markets Nasdaq OMX chief executive Robert Greifeld is determined to mount a counterbid for NYSE Euronext, say people close to him."
"He said the offer created an exit opportunity for APG, which it probably would consider fair value, and means a counterbid in conjunction with Goodman was very unlikely."